SUMMARYIn this paper we consider a parameter estimation procedure for shallow sea models. The method is formulated as a minimization problem. An adjoint model is used to calculate the gradient of the criterion which is to be minimized. In order to obtain a robust estimation method, the uncertainty of the open boundary conditions can be taken into account by allowing random noise inputs to act on the open boundaries. This method avoids the possibility that boundary errors are interpreted by the estimation procedure as parameter fluctuations. We apply the parameter estimation method to identify a shallow sea model of the entire European continental shelf. First, a space-varying bottom friction coefficient is estimated simultaneously with the depth. The second application is the estimation of the parameterization of the wind stress coefficient as a function of the wind velocity. Finally, an uncertain open boundary condition is included. It is shown that in this case the parameter estimation procedure does become more robust and produces more realistic estimates. Furthermore, an estimate of the open boundary conditions is also obtained. KEY WORDS Tidal models Maximum likelihood Modelling uncertain boundaries Parameter estimation

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Abstract:In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system. Key words: Stochastic tidal modeling, parameter identification, model calibration. IntroduetionIn trying to understand processes that are associated with water movements one can make use of a number of techniques. The process can be observed or it can be simulated numerically. The applications can vary from a study the spread of pollutants in shallow waters to the forecast of storm surges in coastal areas. Before a numerical model can be used as an instrument to predict processes accurately, it has to be ascertained that the model is reliable. This can be performed by adjusting the model such that the model outcome represents a series of observations as good as possible. The adjustment of the model implies that some quantities appearing in the formal equations describing the system dynamics must be specified. With respect to these quantities one may think of the geometry, of boundary conditions, of the location of the pollution sources and their intensity or of some empirical parameters. Usually this is called the calibration of the numerical model. In this paper we will give no extensive treatment of the total process of developing a model, but we will describe a procedure to perform the calibration automatically. Up till now there was no such procedure. This does not mean that, based on an extensive experience, the calibration could not be done accurately by hand. Moreover, it is not at forehand guaranteed that the calibration results of a systematic procedure will be significantly better. However, calibrating a model by hand is very time consuming. Furthermore, using an automatic calibration procedure models can also be developed by less experienced users and finally the results of different calibration sessions can be compared. This is important since the available measurement infor~nation is usually too small

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